A waveplate is also referred to as a linear phase retarder, or as a retarder plate. A waveplate introduces a phase shift between polarized components of light transmitted through the plate. It functions in an optical system to modify and control the relative phase of each constituent beam.
A waveplate is a body of birefringent material in which the ordinary ray and the extraordinary ray travel at different velocities. Consequently, one ray is retarded relative to the other. The path difference k.lambda., in wavelengths, between the two rays is given by EQU k.lambda.=.+-.l (n.sub.e -n.sub.o) where
n.sub.e =refractive index of the extraordinary ray,
n.sub.o =refractive index of the ordinary ray,
l=physical thickness of the plate, and
.lambda.=wavelength of the light ray.
"k" can be considered the retardation expressed in fractions of a wavelength. The phase difference between two rays traveling through a birefringent material is 2.pi./.lambda. times the path difference. Therefore, the phase difference, called the plate retardation .delta., may be expressed as, ##EQU1## Thus, if a phase difference ##EQU2## is introduced between the ordinary and extraordinary rays, the plate is termed a quarter-wave plate. The same characterization is true for any condition expressed by (2.pi.)m+.delta. when "m" is an integer. When "m" is zero, the term zero-order waveplate is used; when "m" is other than zero, the plate is termed a multiple order waveplate.
The simplest retardation plate is a slice cut out of a uniaxial crystal, the slice being cut so that the optic axis lies in a plane parallel to the face of the plate. Heretofore, the principal materials used in waveplate production were crystalline materials such as quartz, calcite and mica. These crystalline materials are well recognized as being highly birefringent. Because of their large birefringent values, the thickness of a zeroth order waveplate would necessarily be impractically thin. For example, the thickness of such a plate would be on the order of 25 microns. Therefore, a practical waveplate, produced from such crystalline materials, must be of a higher order, that is, a multiple of 2.pi. plus the phase difference.
A recent publication by P. D. Hale and G. W. Day, "Stability of Birefringent Linear Retarders (Waveplates)", Applied Optics, 27(24), 5146-53(1988), discusses various types of waveplates and their features. In particular, the publication discusses how retardance in the various types varies with temperature, angle of light ray incidence and wavelength. For example, the effect of a slight deviation in angle of incidence is magnified by the multiple order of retardation inherent in an integral, crystalline waveplate. The term "integral" indicates a unitary, crystalline waveplate composed of a single material.
The authors conclude that, for a waveplate application requiring high stability, a low order, and ideally zero order, waveplate should be chosen. Since a zero-order, integral plate is impractically thin, it is common practice to resort to compound waveplates. Thus, to obtain a 30.degree. retardation (quarter-wave), a positive plate of 360.degree.+30.degree. is sealed to a negative plate of 360.degree.. This provides the desired 30.degree. retardation required with the multiple orders cancelling out.
The authors of the publication discuss problems encountered with prior compound waveplates, and propose a novel, four unit, compound plate. All such compound plates suffer from the fact that they are time-consuming, and hence expensive, to produce. Also, inherently, a crystalline waveplate must be flat, as determined by the rigid, three-dimensional, crystal lattice. For some applications, however, a waveplate in the form of a compound curvature may be advantageous.
It has also been proposed to produce waveplates from organic plastic materials, and such products are commercially available. Such materials are limited to low temperature applications, of course. They also are susceptible to instability from atmospheric moisture, and must be protected from dust in the environment since they are soft and easily scratched in cleaning.